A087950 - OEIS

A087950

Numerators k for which the partial quotients of the k-CF of sqrt(2) are periodic, where a k-CF is defined as the continued fraction representation having k as the constant numerator: x = q_0 + k/(q_1 + k/(q_2 + k/(q_3 +...))).

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 15, 17, 18, 20, 21, 25, 29, 30, 34, 35, 40, 41, 42, 45, 50, 51, 55, 58, 60, 63, 65, 68, 70, 84, 85, 87, 99, 102, 116, 119, 126, 136, 145, 153, 169, 170, 174, 187, 189, 198, 203, 204, 221, 232, 238, 239, 252, 255, 261, 272, 289, 290, 297

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OFFSET

1,2

COMMENTS

It is well-known that quadratic numbers have periodic partial quotients in simple continued fractions where the numerators are 1; it is unexpected that similar expressions of quadratics do not remain periodic for most constant numerators k>1.

LINKS

Table of n, a(n) for n=1..63.

CROSSREFS

Cf. A087951.

Sequence in context: A361202 A284831 A261040 * A060527 A152493 A229028

Adjacent sequences: A087947 A087948 A087949 * A087951 A087952 A087953

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 16 2003

STATUS

approved